Skechers USA Inc. will pay $40 million to settle charges by the Federal Trade Commission that the footwear company made unfounded claims that its Shape-ups shoes would help people lose weight and strengthen their butt, leg and stomach muscles.

Kardashian, Burke and other celebrities endorsed the shoes in Skechers ads.

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The company will pay an addition $5 million to 44 states listed in the lawsuit, including New York.

Wednesday’s settlement also involves the company’s Resistance Runner, Toners, and Tone-ups shoes. Skechers made deceptive claims about those shoes, too, says the agency.

Consumers who bought the shoes will be eligible for refunds, though it’s not clear how much money people will get. The FTC says that will depend on how many claims are received in the eight-month filing period. Most of the $40 million will be returned to consumers, the commission said. A small amount of the money will be used to administer the payouts.

“The FTC’s message, for Skechers and other national advertisers, is to shape up your substantiation or tone down your claims,” said David Vladeck, director of the agency’s consumer protection bureau. For millions of consumers, he said, “the only thing that got a workout was their wallet.”

The commission settled similar charges with Reebok last year over its EasyTone walking shoes and RunTone running shoes. That $25 million agreement also provided customer refunds.

Skechers billed its Shape-ups as a fitness tool designed to promote weight loss and tone muscles with the shoe’s curved “rocker” or rolling bottom — saying it provides natural instability and causes the consumer to “use more energy with every step.” Shape-ups cost about $100 and are sold at retailers nationwide.

Ads for the Resistance Runner shoes claimed people who wear them could increase “muscle activation” by up to 85 percent for posture-related muscles and 71 percent for one of the muscles in the buttocks, said the FTC.

The commission says Skechers falsely represented that clinical studies backed up the company’s claims about its toning shoes. The settlement bars Skechers from misrepresenting any tests, studies or research on its shoes in the future.

In Wednesday’s court filing, Skechers says it disputes the charges and is pursuing additional studies. A call to Skechers seeking additional comment was not immediately returned.

The settlement is part of a broader agreement also announced Wednesday — a settlement resolving a multi-state investigation led by the attorneys general from Tennessee and Ohio and involving more than 40 states. The company, based in Manhattan Beach, Calif., will provide $40 million for customer refunds in the federal case and $5 million to the states.